The first sentence above is, for a physicist, the key result. It says that, for the most common way one could modify gravity to incorporate a new force-mediator, the new interaction has to turn on at distances shorter than 39 microns.

At distances longer than that, these measurements show that gravity acts, and in a way that roughly follows the inverse-square law. (at distances of ~100 microns it very-much follows the ISL, and at distances longer than that, it really follows the ISL).

The easy way to think about this result: we are on the cusp of showing that gravity acts over distances shorter than the width of a human hair. Only the finest human hairs are smaller in diameter.

For many years, my goal in life (see HN handle) was to push this limit below 10-microns. Turns out that is really hard to do :).